The Weapon Mastery system will reward players with cool loot (such as charms that hang from weapons and emblems that signify their skill with a certain weapon).

Charms

Mastery Emblems

This new progression system is currently only available on PC but it will come to consoles too at a later date.

PUBG - New Feature - Weapon Mastery

The video above summarizes everything new added to the game with this system.

From the official website:

You can progress through Weapon Mastery levels by earning Weapon XP in matches. Hitting difficult shots, surviving longer and defeating more enemies will all earn you Weapon XP at a faster rate. After every ten levels on a weapon, you will be promoted to the next Mastery Tier (there are 10 tiers total). Gaining levels and tiers in Weapon Mastery will result in unlocking the rewards content the system has to offer. The farther you progress, the more there is to unlock. In order to help you track your progression, we’ve included a new Last Match screen where you can see your earned Weapon XP, weapon stats, and earned rewards from the previous game you’ve played.